This essay considers the origins of the arithmological genre, the first specimen of which was an anonymous Neopythagorean treatise of the first century BCE. Arithmology as a special genre of philosophical writings dealing with the properties of the first ten numbers should be distinguished from number symbolism, which is a universal cultural phenomenon related to individual significant numbers. As our analysis shows, the philosophical foundations of arithmology were laid down in the treatise of Plato’s successor Speusippus On Pythagorean Numbers, who (...) relied on the Platonic doctrine of the ten ideal numbers, whereas in ancient Pythagoreanism arithmological notions, unlike number symbolism, are not attested. In the first century BCE, an epoch of revival of Platonism and Aristotelianism, Speusippus’ ideas received a second birth, thus marking the beginning of arithmology as a popular genre. (shrink)

At the centre of the monograph (1984, first edition) lies a detailed interpretation and critique of the idea of the Good in the Republic. The main thesis of the interpretation runs as follows: The idea of the Good functions as a third item between thinking and being. The main purpose of the monograph is to introduce the systematic problem of the third item via the historical problem of the idea of the Good. The second, enlarged edition (1989) gives a new (...) reconstruction of an "exasperatingly difficult but ever fascinating topic" (H. Cherniss), that is, of the platonic theory of the ideal numbers and the two principles that were contained in the “so-called unwritten doctrines” (Aristotle). The final chapter gives new information on the reception of Plato's idea of the Good in P. Natorp and M. Heidegger. It also includes an updated bibliography. The third edition (2015) is a reprint of the second edition of 1989. Further remarks and an updated bibliography to 2005 are to be found in: - Ferber, Rafael (2005). Ist die Idee des Guten nicht transzendent oder ist sie es doch? Nochmals Platons ΕΠΕΚΕΙΝΑ ΤΗΣ ΟΥΣΙΑΣ. In: Barbaric Damir: Platon über das Gute und die Gerechtigkeit / Plato on Goodness and Justice / Platone sul Bene e sulla Giustizia. Würzburg, 149-174. - Ferber, Rafael / Damschen, Gregor (2015). Is the Idea of the Good Beyond Being? Plato's "epekeinea tês ousias" Revisted (Republic, 6, 509b8-10). In: Nails, Debra; Harold, Tarrant; Kajava, Mika; Salmenkivi, Eero. Second Sailing: Alternative Perspectives on Plato. Espoo, 197-203. (shrink)

CHAPTER ONE LIFE The extant evidence about Speusippus' life is scanty, and little of it is reliable. The reasons are not difficult to discover : the greater ...

At the centre of the monograph (1984, first edition) lies a detailed interpretation and critique of the idea of the Good in the Republic. The main thesis of the interpretation runs as follows: The idea of the Good functions as a third item between thinking and being. The main purpose of the monograph is to introduce the systematic problem of the third item via the historical problem of the idea of the Good. The second, enlarged edition (1989) gives a new (...) reconstruction of an "exasperatingly difficult but ever fascinating topic" (H. Cherniss), that is, of the platonic theory of the ideal numbers and the two principles that were contained in the “so-called unwritten doctrines” (Aristotle). The final chapter gives new information on the reception of Plato's idea of the Good in P. Natorp and M. Heidegger. It also includes an updated bibliography. The third edition (2015) is a reprint of the second edition of 1989. Further remarks and an updated bibliography to 2005 are to be found in -/- Ferber, Rafael (2005). Ist die Idee des Guten nicht transzendent oder ist sie es doch? Nochmals Platons ΕΠΕΚΕΙΝΑ ΤΗΣ ΟΥΣΙΑΣ. In: Barbaric Damir: Platon über das Gute und die Gerechtigkeit / Plato on Goodness and Justice / Platone sul Bene e sulla Giustizia. Würzburg, 149-174.:www.zora.uzh.ch/34098/. (shrink)

Presocratic philosophy, for all its diverse features, is united by the quest to understand the origin and nature of the world. The approach of the Pythagoreans to this quest is governed by their belief, probably based on studies of the numerical relations in musical harmony, that number or numerical structure plays a key role for explaining the world-order, the cosmos. It remains questionable to what extent the Pythagoreans, by positing number as an all-powerful explanatory concept, broke free from Presocratic ideas (...) that certain stuffs or material elements sufficed to account for the source and constitution of the world, but apparently number found such a universal application with them that Aristotle could summarize the Pythagorean position as ‘numbers…are the whole universe’. Historians of Greek philosophy have generally accepted Aristotle's assessment. Of late, however, certain scholars have argued that the Pythagorean number doctrine is Aristotelian interpretation, unjustly foisted upon the Pythagoreans. Enlisted in support of their arguments are the fragments of Philolaus of Croton. Here we have the foremost representative of fifth-century Pythagoreanism, who states as his basic principles, not numbers exactly, but ‘limiters’ and ‘unlimiteds’, and who, it is argued, regards number solely as an epistemological aid for understanding the structure of reality. So Philolaus is called upon as a witness against Aristotle. The rationale goes something like this: Aristotle most likely had written sources for his knowledge of Pythagorean teachings; the only texts we know of with any certainty are Philolaus' book and the writings of Archytas; since Aristotle treats Archytas separately, he is mainly relying on Philolaus; because Philolaus does not expressly state that things are numbers, Aristotle's interpretation is wrong. (shrink)

Joe Sachs has followed up his brilliant translation of Aristotle's Physics with a new translation of Metaphysics. Sachs's translations bring distinguished new light onto Aristotle's works, which are foundational to history of science. Sachs translates Aristotle with an authenticity that was lost when Aristotle was translated into Latin and abstract Latin words came to stand for concepts Aristotle expressed with phrases in everyday Greek language. When the works began being translated into English, those abstract Latin words or their cognates were (...) used, thus suggesting a level of jargon and abstraction, and in some cases misleading interpretation, which was not Aristotle's language or style. These important new translations open up Aristotle's original thought to readers. (shrink)

This two-part volume collects the complete fragments and most important testimonies for the leading presocratic philosophers. The Greek and Latin texts are translated on facing pages and accompanied by a brief commentary for each philosopher.

A fascinating portrait of the Pythagorean tradition, including a substantial account of the Neo-Pythagorean revival, and ending with Johannes Kepler on the threshold of modernism.

In ancient tradition, Pythagoras emerges as a wise teacher, an outstanding mathematician, an influential politician, and as a religious and ethical reformer. This volume offers a comprehensive study of Pythagoras, Pythagoreanism, and the early Pythagoreans through an analysis of the many representations of the individual and his followers.

For the first English edition of his distinguished study, Weisheit und Wissenschaft: Studien zu Pythagoras, Philoloas und Platon, Mr. Burkert has extensively ...

Monte Johnson examines one of the most controversial aspects of Aristiotle's natural philosophy: his teleology. Is teleology about causation or explanation? Does it exclude or obviate mechanism, determinism, or materialism? Is it focused on the good of individual organisms, or is god or man the ultimate end of all processes and entities? Is teleology restricted to living things, or does it apply to the cosmos as a whole? Does it identify objectively existent causes in the world, or is it merely (...) a heuristic for our understanding of other causal processes? Johnson argues that Aristotle's aporetic approach drives a middle course between these traditional oppositions, and avoids the dilemma, frequently urged against teleology, between backwards causation and anthropomorphism. Although these issues have been debated with extraordinary depth by Aristotle scholars, and touched upon by many in the wider philosophical and scientific community as well, there has been no comprehensive historical treatment of the issue. Aristotle is commonly considered the inventor of teleology, although the precise term originated in the eighteenth century. But if teleology means the use of ends and goals in natural science, then Aristotle was rather a critical innovator of teleological explanation. Teleological notions were widespread among his predecessors, but Aristotle rejected their conception of extrinsic causes such as mind or god as the primary causes for natural things. Aristotle's radical alternative was to assert nature itself as an internal principle of change and an end, and his teleological explanations focus on the intrinsic ends of natural substances - those ends that benefit the natural thing itself. Aristotle's use of ends was subsequently conflated with incompatible 'teleological' notions, including proofs for the existence of a providential or designer god, vitalism and animism, opposition to mechanism and non-teleological causation, and anthropocentrism. Johnson addresses these misconceptions through an elaboration of Aristotle's methodological statements, as well as an examination of the explanations actually offered in the scientific works. Reviewed in: Notre Dame Philosophical Review 2006.06.15; Bryn Mawr Classical Review 2006.08.37; Il-Sole – 24 Ore 6 Aug. 2006; Philosophy in Review 26 (2006): 360-2; Rhizai 3 (2006): 171-8; Journal of the History of Philosophy 45 (2007): 323-4; Ancient Philosophy 27 (2007): 191-200; Phronesis 52 (2007): 248-9; Isis 98 (2007): 375; Aestimatio 4 (2007) 146-152; The British Journal for the History of Science 41 (2008): 129-130. The European Legacy 14 (2009); La Cultura 47 (2009): 174-175; Sean M. Row, Teleology in Political Contexts: an assessment of Monte Ransome Johnson’s “Aristotle on Teleology”. (A thesis presented to the faculty of the college of arts and sciences of Ohio University, 2009.). (shrink)

This is the first book to analyze systematically crucial aspects of ancient Greek philosophy in their original context of mystery, religion, and magic. The author brings to light recently uncovered evidence about ancient Pythagoreanism and its influence on Plato, and reconstructs the fascinating esoteric transmission of Pythagorean ideas from the Greek West down to the alchemists and magicians of Egypt, and from there into the world of Islam.

Presocratic philosophy, for all its diverse features, is united by the quest to understand the origin and nature of the world. The approach of the Pythagoreans to this quest is governed by their belief, probably based on studies of the numerical relations in musical harmony, that number or numerical structure plays a key role for explaining the world-order, the cosmos. It remains questionable to what extent the Pythagoreans, by positing number as an all-powerful explanatory concept, broke free from Presocratic ideas (...) that certain stuffs or material elements sufficed to account for the source and constitution of the world, but apparently number found such a universal application with them that Aristotle could summarize the Pythagorean position as ‘numbers…are the whole universe’ . Historians of Greek philosophy have generally accepted Aristotle's assessment. Of late, however, certain scholars have argued that the Pythagorean number doctrine is Aristotelian interpretation, unjustly foisted upon the Pythagoreans. Enlisted in support of their arguments are the fragments of Philolaus of Croton. Here we have the foremost representative of fifth-century Pythagoreanism, who states as his basic principles, not numbers exactly, but ‘limiters’ and ‘unlimiteds’, and who, it is argued, regards number solely as an epistemological aid for understanding the structure of reality. So Philolaus is called upon as a witness against Aristotle. The rationale goes something like this: Aristotle most likely had written sources for his knowledge of Pythagorean teachings; the only texts we know of with any certainty are Philolaus' book and the writings of Archytas; since Aristotle treats Archytas separately, he is mainly relying on Philolaus; because Philolaus does not expressly state that things are numbers, Aristotle's interpretation is wrong. (shrink)

This five-volume edition of Aristotle's works in Greek is (with the exception of Vol. III) a photomechanical copy of the standard edition of Aristotle's works from 1831-1870. Vols. I And II contain Aristotle's works. VOlume III presents O. GIgon's revision and supplementation of Aristotle's fragments. VOl. IV Presents a selection of the most important sections of Classical commentaries on Aristotle, together with a concordance with the Commentaria in Aristotelem Graeca. VOl. V Contains a copy of H. BOnitz' Index Aristotelicus.

: In this paper we give a detailed reconstruction of the first chapter of De Caelo I.1. Aristotle attempts to prove there that bodies are complete and perfect in virtue of being extended in three dimensions. We offer an analysis of this argument and argue that it gives important insight into the role the notion of body plays in physical science. Contrary to other interpretations, we argue that it is an argument about physical, as opposed to mathematical, bodies and that (...) the perfection and completeness of bodies is due to their nature. Moreover, Aristotle heavily relies in his proof on the premise that the number three implies perfection, a view he ascribes to the Pythagoreans. We review the possible sources of this view, as well as its role in Aristotle’s argumentative strategy. (shrink)

Excerpt from La Théorie Platonicienne des Idées Et des Nombres d'Après Aristote: Étude Historique Et Critique La théorie phtonioionno de l'amour. Vol. Ia-8 de la Collection historique des grands philosophes 3 fr. 75. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the (...) aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Was Plato a Pythagorean? Plato's students and earliest critics thought so, but scholars since the nineteenth century have been more skeptical. With this probing study, Phillip Sidney Horky argues that a specific type of Pythagorean philosophy, called "mathematical" Pythagoreanism, exercised a decisive influence on fundamental aspects of Plato's philosophy. The progenitor of mathematical Pythagoreanism was the infamous Pythagorean heretic and political revolutionary Hippasus of Metapontum, a student of Pythagoras who is credited with experiments in harmonics that led to innovations in (...) mathematics. The innovations of Hippasus and other mathematical Pythagoreans, including Empedocles of Agrigentum, Epicharmus of Syracuse, Philolaus of Croton, and Archytas of Tarentum, presented philosophers like Plato with novel ways to reconcile empirical knowledge with abstract mathematical theories. Plato and Pythagoreanism demonstrates how mathematical Pythagoreanism established many of the fundamental philosophical questions Plato dealt with in his central dialogues, including Cratylus, Phaedo, Republic, Timaeus, and Philebus. In the process, it also illuminates the historical significance of the mathematical Pythagoreans, a group whose influence on the development of philosophical and scientific methods has been obscured since late antiquity. The picture that results is one in which Plato inherits mathematical Pythagorean method only to transform it into a powerful philosophical argument about the essential relationships between the cosmos and the human being. (shrink)

Diese fünfbändige Aristoteles-Ausgabe in griechischer Sprache ist (mit Ausnahme von Bd III) ein fotomechanischer Nachdruck der maßgeblichen Aristoteles-Ausgabe von 1831-1870. Band I und II enthält die Werke Aristoteles. In Band III wird die durch O. Gigon besorgte Bearbeitung und Ergänzung der Fragmente des Aristoteles wiedergegeben. Band IV bietet eine Auswahl der bedeutendsten Stücke aus den antiken Kommentaren zu Aristoteles, sowie eine Konkordanz mit den Commentaria in Aristotelem Graeca. In Band V ist der Index Aristotelicus von H. Bonitz nachgedruckt.